I mean for the bi-invariant metric (but actually any metric would work). In this metric geodesics are translates of 1-parameter subgroups so we need only to show that $exp(t X)$ for any X in the lie algebra is a closed curve. Then we can use the standard forms (like the Jordan form) for matrices. My source of doubt comes from the fact that these groups don't seem to be on the list of Riemannian manifolds with periodic geodesic flow.